6 computing gunsight, hud and hms

Computing GunsightHead Up Displays &

Head Mounted Displays

SOLO HERMELIN

Updated: 01.12.12

1

Table of Content

SOLO

2

Computing Gunsight

Introduction

SOLO

3

Computing Gunsight

The basic material of this document was prepared between 1972 – 1973, when, as a part of my duty as an IAF Officer, was the Maintenance of Lead Computing Optical Sight Sensor (LCOSS) ASG-22, and ASG-26, Gyro Gunsight, of the F4 Phantom.

The task of the LCOSS was to help the pilot to point the Aircraft Fixed Gunin such a way, that the fired projectiles will intercept the flying Target.

SOLO Lead Computing Gunsight

A gyro gunsight (G.G.S.) is a modification of the non-magnifying reflector sight in which target lead (the amount of aim-off in front of a moving target) and bullet drop are allowed for automatically, the sight incorporating a gyroscopic mechanism that computes the necessary deflections required to ensure a hit on the target. The sight was developed just before the Second World War for aircraft use during aerial combat.

Gyro Gunsight (G.G.S.)

The Ferranti Gyro Sight Mk IIc

Gyro gunsights were (for the most part) modifications of the reflector gunsight to aid pilots in hitting targets (other aircraft) that were turning rapidly in front of them. The reflector sight (first used on German fighters in 1918[1] and widely adopted on all kinds of fighter and bomber aircraft in the 1930s) was an optical device consisting of a 45 degree angle glass beam splitter that sat in front of the pilot and projected an illuminated image of an aiming reticule that appeared to sit out in front of the pilot's field of view at infinity and was perfectly aligned with the plane's guns ("boresighted" with the guns). The optical nature of the reflector sight meant it was possible to feed other information into field of view, such as modifications of the aiming point due to deflection determined by input from a gyroscope.[2]

It is important to note that the information presented to the pilot was of his own aircraft, that is the deflection/lead calculated was based on his own bank-level, rate of turn, airspeed etc. The assumption was that the flight-path was following the flight-path of the target aircraft, as in a dogfight, therefore the input data was close-enough

History

Optical system of Gyro Sight

http://en.wikipedia.org/wiki/Gyro_gunsight


http://en.wikipedia.org/wiki/File:Gyro_Sight_Mk_IIc_Ferranti.jpg



History (continue – 1)

After tests with two experimental gyro gunsights which had begun in 1939, the first production gyro gunsight was the British Mark I Gyro Sight , developed at Farnborough in 1941. To save time in development the sight was based on the already existing type G prismatic sight, basically a telescopic gun sight folded into a shorter length by a series of prisms.[3] Prototypes were tested in a Supermarine Spitfire and the turret of a Boulton Paul Defiant in the early part of that year. With the successful conclusion of these tests the sight was put into production by Ferranti, the first limited-production versions being available by the spring of 1941, with the sights being first used operationally against Luftwaffe raids on Britain in July the same year. The Mark I sight had a number of drawbacks however, including a limited field of view, erratic behavior of the reticle, and requiring the pilot/gunner to put their eye up against an eyepiece during violent maneuvers.Production of the Mark I was postponed and work started on an improved sight. Changes involved incorporating the gyro adjusted reticle into a more standard reflector sight system. This new sight became the Mark II Gyro Sight, which was first tested in late 1943 with production examples becoming available later in the same year. In the Mark II the pilot had to set the wingspan of the target, and use a throttle mounted control to keep the target centered

British Developments

The Mark II was also subsequently produced in the US by Sperry as the K-14 (USAAF) and Mk18 (Navy)The radar-aimed AGLT Village Inn tail turret incorporated a Mark II Gyro Sight and this turret was fitted to some Lancaster bombers towards the end of World War II.





Mark II Gyro Sight demonstration on the Spitfire

The Mark II Gyro Gunsight was the first gyroscopic gunsight to see widespread service with the RAF. It was first tested in late 1943 with production examples becoming available later in the same year. The Mark II was also subsequently produced in the United States as the K-14 (USAAF) and Mk18 (Navy).

Spitfire Mk.IX gyro sight trial, Il-2 Sturmovik _46, Movie

http://www.youtube.com/watch?v=0SBE1hRVdQY




German Developments

Although since 1935 the relevant German companies offered the Reich Air Ministry (RLM) a new type of gyro-stabilized sight, the well-proven REVI (Reflexvisier, or reflector sight) remained in service for combat aircraft. The gyro-stabilized sights received an additional designation of EZ (Einheitszielvorrichtung, or Target Predictor Units), such as EZ/REVI-6a. The development of the EZ 40 gyro sight began in 1935 at the Carl Zeiss and Askania companies, but was of low priority. Not until the beginning of 1942, when a US P-47 Thunderbolt fighter equipped with a gyro-stabilised sight was captured, did the RLM speed up research. In the summer of 1941, the EZ 40, for which both the Carl Zeiss and Askania companies were submitting their developments, was rejected. Tested in a Bf 109 F, Askania's EZ 40 produced 50 to 100% higher hit probability compared to the then standard sight, the REVI C12c.[5] In the summer of 1943 an example of the EZ 41 developed by the Zeiss company was tested, but was refused because of too many faults. In the summer 1942, the Askania company began work on the EZ 42, which gunsight could be adjusted for the target's wingspan (in order to estimate distance to the target). Three examples of the first series of 33 pieces were delivered in July 1944. These were followed by further 770 units, the last being delivered by the beginning of March 1945. Each unit took 130 labour hours to produce. The EZ 42 was made up by two major parts, and lead computation was provided by two gyroscopes. The system, weighing 13.6 kg (30 lb) complete, of which the reflector sight was 3.2 kg, was ordered into mass production at the Steinheil company in Munich. Approximately 200 of the sights were installed into Fw 190 and Me 262 fighters for field testing. The pilots reported that attacks from 20 degrees deflection were possible, and that although the maximum range of the EZ 42 was stated as approximately 1,000 meters, several enemy aircraft were shot down from a combat distance of 1,500 meters.[6]

The EZ 42 was compared with the Allied G.G.S. captured from in a P-47 Thunderbolt in September 1944 in Germany. Both sights were tested in the same Fw 190, and by the same pilot. The conclusion was critical of the moving graticule of the G.G.S., which could be obscured by the target. Compared to the EZ 42, the Allied sight's prediction angle was found on average to be 20% less accurate, and vary by 1% per degree. Tracking accuracy with the G.G.S. measured as the mean error of the best 50% of pictures was 20% worse than with the EZ 42

The German [HD], Movie


SOLO

8

Lead Computing Gunsight

Lockheed Martin has developed from its earlier equipment an improved lead-computing optical sight that enables air-to-air combat to be conducted without the need for continuous target tracking. This capability is incorporated in the system for the US Air Force McDonnell Douglas F-4E.The AN/ASG-26A comprises a head-up display, two-axis lead-computing gyroscope, gyro mount and lead-computing amplifier. For airborne targets the system displays gun and missile fire-control information by means of a servoed aiming mark. Against ground targets the pilot adjusts the aiming mark manually to control gun, rocket and bombing displays.The aircraft's own manoeuvres generate rate and acceleration signals in the gyro lead-computer. Range to target is measured by radar, and angle of attack, air density and the airspeed needed for trajectory correction are supplied by the air data computer. With these parameters fed into the system, the aiming reference is displaced so as to produce the appropriate lead angle and gravity corrections. Analogues of roll angle and range are also projected onto the combining glass. In ground attack modes other sensors generate corrections for drift and offset bombing is also possible

AN/ASG-26A Lead-computing optical sight (United States), FLIGHT/MISSION MANAGEMENT (FM/MM) AND DISPLAY SYSTEMS

Operational status In service in the McDonnell Douglas F-4E, but no longer in production.


F4 Phantom gun direction

AAA VV 1=

BSTmm VV 1=

L = Kinematic Lead Angle

ProjectilePath

Target Position at Projectile

Shoot

Target Predicted Flight

Path

Projectile-TargetIntercept

Point

fTTV

a - Angle of Attack

Line of Sight through

Reticle Image

SD12/2fTTV

2/1 2

fZTg−

In the Lead Mode, the Pilot maneuvers the Aircraft to keep the Pipper (Optical Sight)On the Target for at least half a second and then he pushes the Gun Trigger to fire aVolley of Projectiles. The Gunsight computes the Lead of Aircraft Boresight (Gun Direction) such that some of the Volley Projectiles will Hit the Target.


AV - Aircraft True Airspeed (TAS)

mV - Muzzle Velocity of the Projectile

PV

- Mean Total Projectile Velocity

BmAA

BmAABfAABfAAP

VV

VVVVVVV

11

111111

+

++=+=

fV - Mean Projectile Velocity Relative to Aircraft in Boresight (Gun) Direction

B1

fABfAA VVVV +≈+ 11 mABmAA VVVV +≈+ 11( )BmAA

mA

fAP VV

VV

VVV 11 +

++

=

- Distance to Target in Direction D S1

- Target Velocity VectorTV ( )

td

dD

td

DdVD

td

dVV S

SAASAAT

11111 ++=+=

Target – Projectile Hit Equation: ( )∫ ⋅−−= fT

ZTPS tdtgVVD0

11


AAA VV 1=

BSTmm VV 1=


ProjectilePath


Shoot


Path


Point

fTTV

a - Angle of Attack


Reticle Image

SD12/2fTTV

2/1 2

fZTg−


( )BmAAAm

AfP VV

VV

VVV 11 +

++

=

- Target Velocity VectorTV ( )

td

dD

td

DdVD

td

dVV S

SAASAAT

11111 ++=+=

Target – Projectile Hit Equation: ( )∫ ⋅−−= fT

ZTPS tdtgVVD0

11

PV

- Mean Total Projectile Velocity

( )

( )

( )∫

∫

∫

∫

⋅−−−−

+−

+=

⋅−−−

+⋅−⋅−⋅+⋅

+−+−

=

⋅−−−

++

++−

−=

⋅−−−−+

++

=

f

f

f

f

T

ZSSABAAm

fmBf

T

ZSSBAm

fAmAmAmfABA

Am

fm

T

ZSSBmAm

AfAA

Am

fm

T

ZSSABmAAmA

fAS

tdtgDDVVV

VVV

tdtgDDVV

VVVVVVVVV

VV

VV

tdtgDDVVV

VVV

VV

VV

tdtgDDVVVVV

VVD

0

0

0

0

111111

111111

11111

111111

Assuming that Tf is small and all the expressions in the integral are constant, we obtain:

( ) Zf

SfSfABfAAm

fmBffS

TgTDTDTV

VV

VVTVD 1

2111111

2

⋅−−−−+−

+=


AAA VV 1=

BSTmm VV 1=


ProjectilePath


Shoot


Path


Point

fTTV

a - Angle of Attack


Reticle Image

SD12/2fTTV

2/1 2

fZTg−


Target – Projectile Hit Equation:

( ) Zf

SfSfABfAAm

fmBffS

TgTDTDTV

VV

VVTVD 1

2111111

2

⋅−−−−+−

+=

Let multiply this equation by (vector product)×S1

( ) ZSf

SSfSSfABSfAAm

fmBSffSS

TgTDTDTV

VV

VVTVD 11

211111111111

2

00

×⋅−×−×−−×+−

+×=×

Since defineLLSB ≈=× sin11 LSB

=× :11

Define the Line-of-Sight Rate.SS 11: ×=Λ

( ) ( )( ) ( )( ) αα ≈−⋅≈−⋅−=−× ABSABSABABS 11,1sin11,1sin11111We have

Define ( ) α=−× :111 ABS

ZSf

ffAAm

fmff

TgTDTV

VV

VVLTV 11

20

2

×⋅−Λ−+−

+−= αWe obtain

ZSf

f

f

A

Am

fm

f V

Tg

V

V

VV

VV

V

DL 11

2×

⋅⋅

−⋅+−

+Λ−= αor


AAA VV 1=

BSTmm VV 1=


ProjectilePath


Shoot


Path


Point

fTTV

a - Angle of Attack


Reticle Image

SD12/2fTTV

2/1 2

fZTg−


Target – Projectile Hit Equation:

ZSf

f

f

A

Am

fm

f V

Tg

V

V

VV

VV

V

DL 11

2×

⋅⋅

−⋅+−

+Λ−= α

Assume a Coordinated Turn of the Aircraft ay a constant True Airspeed Va:

ZNtotal gaa 1−=

where is the acceleration normal (to Aircraft Wing Plan)

Na

( ) AAAAAAtot VVV

td

da 111

0

+==≈

( ) NANSANAANtotalZ asVaVsaVsaassg ×−Λ=

−×≈

−×=−×=×− 11111111

NAZ asVsg ×−Λ≈×− 111 N

f

f

f

fAZS

f

f asV

T

V

TV

V

Tg ×⋅

−Λ⋅⋅

≈×⋅⋅

− 122

112

NSf

f

f

A

Am

fmfA

f

aV

T

V

V

VV

VV

D

TV

V

DL

×

⋅−⋅

+−

+Λ⋅

⋅⋅

−⋅−= 122

1 α


AAA VV 1=

BSTmm VV 1=


ProjectilePath


Shoot


Path


Point

fTTV

a - Angle of Attack


Reticle Image

SD12/2fTTV

2/1 2

fZTg−


VR

VCM

SV D

=

⋅⋅−=

2

2

1 ρ

Computation of Time of Flight Tf and Vf:Assume mP, mass of projectile, and CD , the drag coefficient, assumed constant

from which

VCM

S

Rd

VdD⋅⋅−= ρ

2

1 RdCM

S

V

VdD⋅⋅−= ρ

2

1

RCM

S

V

VD

I

⋅⋅−= ρ2

1ln ( ) RC

M

S

mA

RCM

S

I

DD

eVVeVV⋅⋅−⋅⋅−

+==ρρ

2

1

2

1

( ) ( )

DB

DK

fB

mADC

m

S

fD

mAD RC

m

S

f

mAD

favg

Cm

SK

eDK

VVe

DCS

mVVRde

D

VVRdV

DV fBfDf Df

⋅=

−⋅⋅⋅

+=

−⋅

⋅⋅⋅⋅+⋅=+== −⋅⋅−⋅⋅−

∫∫

2

1:

1121 2

1

0

2

1

0

ρρρ

ρρ

( ) ( ) ( ) fmABmAfBfBfB

mAA

DK

fB

mAAavgf DVVKVVDKDK

DK

VVVe

DK

VVVVV fB ⋅+⋅⋅⋅−≈−

+⋅⋅⋅−⋅⋅+−⋅

⋅⋅+≈−−⋅

⋅⋅+=−= − ρρρ

ρρρ

2

1

2

1111: 2


Computation of Time of Flight Tf and Vf (continue – 1)

( ) fmABmAavgf DVVKVVVV ⋅+⋅⋅⋅−≈−= ρ2

1:

( ) ∫∫ +=+= ff T

TS

T

Zf tdVDtdgVD00

11

( ) ffAfavg

T

f TVVTVtdVDf ⋅+=⋅=≈ ∫0

( ) fA

T

SSA

T

TSf TDVDtdDDVDtdVDDff ⋅++≈

+++≈+= ∫∫

00111

( ) ( ) ( ) 0=−⋅−⇒⋅++≈⋅+≈ DTDVTDVDTVVD fffAffAf

( ) ( )[ ] 02

1 =−⋅

−⋅++⋅+⋅⋅⋅− DTDTDVDVVKV f

D

fAmABm

f

ρ


Computation of Time of Flight Tf and Vf (continue – 2)

( ) ( )[ ] 02

1 =−⋅

−⋅++⋅+⋅⋅⋅− DTDTDVDVVKV f

V

D

fAmABm

f

f

ρ

( ) ( ) ( ) 02

1

2

1 2 =+⋅

+⋅⋅⋅−−⋅+⋅+⋅⋅⋅ DTVVKVTDVVVK f

B

mABmf

A

AmAB

ρρ

A

DABBT f ⋅

⋅⋅−−=2

42

ff TDDV /+=

SOLO

Snap Shot Gunsight

In the Lead Mode of Fire, the Pilot must keep the Pipper on the Target, for a small period of time, and then he starts firing the Gun.

In the Snap Shoot Mode of Fire, the Pilot must bring the Pipper to cross the Target, but must start Firing at least Time of Flight (Tf ) (no more then a second), beforeTarget Crossing. This Mode will work if the Pipper points on the Projectile Position Tf seconds after Firing, so the Projectile (fired Tf before), the Pipper and the Targetcoincide.

The Tf is given as before by the three equations:

( )

( )( )

=−⋅−

⋅++≈

⋅+⋅⋅⋅−≈−=

0

2

1:

DTDV

TDVDD

DVVKVVVV

ff

fAf

fmABmAavgf

ρ

A

DABBT f ⋅

⋅⋅−−=2

42

( ) ( ) ( ) 02

1

2

1 2 =+⋅

+⋅⋅⋅−−⋅+⋅+⋅⋅⋅ DTVVKVTDVVVK f

B

mABmf

A

AmAB

ρρ

Tf is not a function of Target Data, therefore the Pipper doesn’t have to be on Target to compute Tf.

SOLO

Snap Shot Gunsight

In the Snap Shot Mode of Fire, the Pipper is pointed to the Projectile that was firedTf seconds before.

- unit vector given Pipper Direction at Fire.S1

fS1

- unit vector given Pipper Direction at Tf.

∫+=f

f

T

SSS td0

111

During Tf the Aircraft Position, relativeto Projectile Firing is.

( )∫

+

fT

AAAA tdVtd

dtV

0

11

Snap Shoot Gunsight Equation is:

( )ff

fff

SS

T

AAPZ

TT

P KtdVtd

dtVtdtgtdV 111

000

=

+−− ∫∫∫

( )

+=

−−− ∫∫

f

f

f T

SSS

T

AAZAP tdKtdVtd

dttgVV

00

1111 or:

SOLO

Snap Shot Gunsight

In the Snap Shot Mode of Fire, the Pipper is pointed to the Projectile that was firedTf seconds before (continue – 1).

( )

+=

−−− ∫∫

f

f

f T

SSS

T

AAZAP tdKtdVtd

dttgVV

00

1111

( ) ZNAAAAAAtotal gaVVV

td

da 1111

0

−=+==≈

SS

T

SSNAP f

f

fKtdKatVV 11

0

=

−−−∫

As a First Order Assumption, all the vectors in the previous equation, we obtain:

SSfSSfNAfAfP ffKTKTaTVTV 112/1 2

=−−−

( )BmAAmA

fAP VV

VV

VVV 11 +

++

=

SSfSSfNAAAm

fmBm

Am

Af

ffKTKTaV

VV

VVV

VV

VV112/11

=⋅

−−

+−

−++

SOLO

Snap Shot Gunsight


SSfSSf

NAAAm

fmBm

Am

Af

ffKTK

TaV

VV

VVV

VV

VV11

211

=⋅

−−

+−

−++

011112

11111

=×=⋅

×−×−×

+−

−×++

SSSfSSSf

NSASAAm

fmBSm

Am

Af

ffKTK

TaV

VV

VVV

VV

VV

Multiply (Vector Product) this equation byfrom the Left:

S1

We defined:

( ) αα

−−=×⇒

=−×

−=×

Λ=×

LL

AS

ABS

BS

SS

11:111

:11

:11

( ) 02

1

=Λ−×−−−+−

−++

−fS

fNSA

Am

fmm

Am

Af KT

aLVVV

VVLV

VV

VVα

02

1

=Λ−×−+−

+−fS

fNSA

Am

fmf K

TaV

VV

VVLV α

×S1

SOLO

Snap Shot Gunsight


( ) 012

=Λ−×

⋅−

+−

=f

S

NSf

f

f

A

Am

fm

V

Ka

V

T

V

V

VV

VVL fα

Let compute .fSK

From the Figure

( )

N

ff

a

Zf

SSAfAfp gaT

KTVTV 12

112

+++=

fffff SfASSAfANf

SSAfAfpfp KTVKTVaT

KTVTVTV +≈+≈++== 112

112

But we found also that ffAfp TVVTV +=

Therefore andffS TVKf=

( )NSf

f

f

A

Am

fmf a

V

T

V

V

VV

VVTL

×−

+−

+Λ−= 12

α

SOLO

Computing Gunsight

We obtained

( )NSf

f

f

A

Am

fmf a

V

T

V

V

VV

VVTL

×−

+−

+Λ−= 12

α

NSf

f

f

A

Am

fmfA

f

aV

T

V

V

VV

VV

D

TV

V

DL

×

⋅−⋅

+−

+Λ⋅

⋅⋅

−⋅−= 122

1 α Lead Computing

Snap Shot Computing

We can see that the two expression are different only in the first term, and we can write

⋅⋅

−⋅=×

⋅−⋅

+−

+Λ⋅−=ShootSnapT

LeadD

TV

V

D

KaV

T

V

V

VV

VVKL

f

fA

fNSf

f

f

A

Am

fm 21

12

α

Note:The Pilot can use a Snap Shot Gunsight in Lead Mode, since by keeping the Pipperon the Target and Firing for at leas Tf seconds (around a second) the Projectiles willHit the Target.



A Gyro Gunsight (G.G.S.) is composed of a GimbaledDwo Degrees of Freedom Gyro, that Rotation Axis points, when the Aircraft isn’t move, in the Boresight Direction (also Gun direction).• The Optical Pipper of the Gunsight is Slaved to Gyro direction. • In front of the Gyro’s Rotor is a Metallic Disc that rotates with it.• In front of the Metallic Rotating Disc is a Static Electromagnet. The Electromagnetic Field is pointed in the Boresight Direction. It’s Strength is defined by a Current controlled by an Analog Lead Gunsight Computer.• Due to Rotation of the Disc in an Electromagnetic Field, Eddie Currents are induced in the Disc Metallic Surface.• When the Aicraft Maneuvers, the Boresight Direction will change and the Eddie Currents will move, relative to Electromagnetic Field, causing an Electromagnetic Force acting on the Disc, therefore a Moment on the Gimbaled Gyro. • By applying Electromagnet’s Current to satisfy the Lead Angle Equation the Gyro will point in the required direction, and so the Optical Pipper.

⋅⋅

−⋅=×

⋅−⋅

+−

+Λ⋅−=SnapShootT

LeadD

TV

V

D

KaV

T

V

V

VV

VVKL

f

fA

fNSf

f

f

A

Am

fm 21

12

α



Torque of the Eddie Currents

The Gyro’s Metallic Disk rotates in front of the Electromagnet Field. This produces Eddie Currentson the Disk Skin. As long as the Gyro RotationDirection is the same as Electromagnetic FieldDirection the Moment due to Eddie Currents inthe Electromagnetic Field B is zero. When the Aircraft maneuvers ( and relative to ) the Moment due to Eddie Currents is not zero, and thisin turn, will change the Gyro direction .We want to find the relation between the Electromagnetic Field Intensity B, the position of and , and the Torque on the Gyro.

S1

B1

B1 S1

S1 B1

S1



Suppose a small surface of the Rotating Disk(ω), at a distance R from the center of Gyro Gimbal, moving at the velocity u.

The Electromagnetic Field Intensity Vector

BEMB IkBB 11 −=−=

( ) ( ) rSrS RRu 1111 ×−=×−= ωω

Because of the Electromagnetic Field B the free electrons in the Metallic Disk willMove, and produce an Electric Field Intensity

BuE

×=

This will create a Current Intensity in the Disk Skin

BuEj

×==ρρ11

where ρ is the resistance mean value.

Torque of the Eddie Currents (continue – 1)



The Current in the skin surface dS is

The force acting on the Current of length dl due to the Electromagnetic Field B is

SkinSdBuSdjid

×==ρ1


( )

SkinVd

Skin ldSdBBuldBidfd ××=×=ρ1

( ) ( ) 22

0

BuBuBuBBBu

−=−⋅=××

SkinVduB

fd

ρ

2

−=

The Moment on the Gyro is computed by considering the distance from the Center of Gyro Gimbals.

( ) SkinrSr

Skinrr

VdRBR

VduBR

fdRTd

111

11

2

2

×−×−=

×−=×=

ωρ

ρ




( ) SkinrSr VdBR

Td 11122

××=ρ

ω

( ) ( )( ) ( )

( ) ( ) ( ) ( )[ ]( ) ( )

( ) ( ) ( ) ( )rSSrSrSSrSr

rSSrS

rrSSrSrSSrSrS

rSrSrS

rSrSrSr

111111111111

11111

11111111111111

1111111

1111111

2

2

2

××⋅+

⋅−=××

××⋅=

−⋅⋅=

⋅−−⋅−

⋅−=××⋅

⋅−=××

Decompose this in the component in direction (that will be compensate by the Gyro Motor) and that normal to it (that will cause the precession).

S1

( ) ( ) ( )

nSS Td

SkinrSSrS

Td

SkinrSS VdBR

VdBR

Td 11111111122222

××⋅+

⋅−=

ρω

ρω

SOLO Computing Gunsight



The Total Moment normal to Gyro Rotation Axis is

( ) ( )( )BSSCG

V

SkinrSSrSS

IK

VdBR

TSkin

n

111

11111

2

22

××=

××⋅= ∫ω

ρω



⋅⋅

−⋅=×

⋅⋅−⋅

+−

⋅+−=Λ

ΛΛΛSnapShootT

LeadD

TV

V

D

KaV

T

KV

V

VV

VV

KL

Kf

fA

fNSf

f

f

A

Am

fm 21

12

111

321

α

Implementation of LK

11 −=Λ

( )SBKL

K11

111

×−=−=Λ

We want to find the Torque to be applied on the Gyro to obtain this. In steady-state

( ) SSBG

SG

IH

S K

IL

K

IHHT

G

11111111

××=×=×Λ−=×Λ=

= ωωω

( )BSSCGS IKTn

1112 ××= ω

We found that the Moment on the Gyro due toEddie Currents produce by the deflection of the Gyro direction to relative to Electromagnetis

S1 B1

Since ( ) ( ) ( )BSSSBSSSB 111111111

××=××−=××

Equalizing the two expressions we must have2

CGG IKK

I ωω =K

KII GGC =

Implementation of Lead Computation with Gyro Gunsight



⋅⋅

−⋅=×

⋅⋅−⋅

+−

⋅+−=Λ

ΛΛΛSnapShootT

LeadD

TV

V

D

KaV

T

KV

V

VV

VV

KL

Kf

fA

fNSf

f

f

A

Am

fm 21

12

111

321

α

Implementation of

We want to find the Torque to be applied on the Gyro to obtain this.

( )[ ] SABSGSG K

KIIT 1111122

×−×−=×Λ−= αωω

( )ABS

K

f

A

Am

fm

K

K

V

V

VV

VV

K111

1:2

−×=⋅+−

⋅=Λ αα

α

( )[ ]( )

αωω α

α

α

K

KI

K

KIT GSABSG

ABS

=×−×=

≈−

11,1sin

2 1111

( )ABS 111:

−×=αf

A

Am

fm

V

V

VV

VVK ⋅

+−

=:α

Implementation of Lead Computation with Gyro Gunsight (continue – 1)



⋅⋅

−⋅=×

⋅⋅−⋅

+−

⋅+−=Λ

ΛΛΛSnapShootT

LeadD

TV

V

D

KaV

T

KV

V

VV

VV

KL

Kf

fA

fNSf

f

f

A

Am

fm 21

12

111

321

α

Implementation of

We want to find the Torque to be applied on the Gyro to obtain this.

( ) SNSf

fGSG a

V

T

KIIT 11

2

1133

××

⋅⋅=×Λ−= ωω

NSf

f aV

T

K

×⋅

⋅−=Λ 12

1:3

( )( )

f

fNG

aa

SNSf

fG V

T

K

aIa

V

T

KIT

NSN

⋅⋅=××

⋅⋅=

≈

211

2

1

1,1sin

3 ωω




⋅⋅

−⋅=×

⋅⋅−⋅

+−

⋅+−=Λ

ΛΛΛSnapShootT

LeadD

TV

V

D

KaV

T

KV

V

VV

VV

KL

Kf

fA

fNSf

f

f

A

Am

fm 21

12

111

321

α

( ) SNSf

fGSG a

V

T

KIIT 11

2

1133

××

⋅⋅=×Λ−= ωω


is perpendicular to and in the plane definedby and

S1

( )AB 11

−S1

is perpendicular to and in the plane definedby and

S1

Na

S1

Since L and α are small angles, we may say that and are collinear and in theGyro zG direction, therefore

2T

3T

GGG Zf

NfGZZ V

aTK

K

ITTT 1

2132

⋅⋅

+−=≈+ αωα

( )[ ] SABSGSG K

KIIT 1111122

×−×−=×Λ−= αωω



Lead Angle Computing Loops

SOLO Head-up Display (HUD)

A Head-Up Display or heads-up display—also known as a HUD—is any transparent display that presents data without requiring users to look away from their usual viewpoints. The origin of the name stems from a pilot being able to view information with the head positioned "up" and looking forward, instead of angled down looking at lower instruments

A typical HUD contains three primary components: a Projector Unit, a Combiner, and a Video Generation Computer

• The Projection Unit in a typical HUD is an optical collimator setup: a convex lens or concave mirror with a Cathode Ray Tube, light emitting diode, or liquid crystal display at its focus. This setup (a design that has been around since the invention of the reflector sight in 1900) produces an image where the light is parallel i.e. perceived to be at infinity

• The Combiner is typically an angled flat piece of glass (a beam splitter) located directly in front of the viewer, that redirects the projected image from projector in such a way as to see the field of view and the projected infinity image at the same time. Combiners may have special coatings that reflect the monochromatic light projected onto it from the projector unit while allowing all other wavelengths of light to pass through. In some optical layouts combiners may also have a curved surface to refocus the image from the projector

• The Computer provides the interface between the HUD (i.e. the projection unit) and the systems/data to be displayed and generates the imagery and symbology to be displayed by the projection unit

SOLO Head-up Display (HUD)

Collimating Optics

SOLO Head-Mounted Display (HMD)

Other than fixed mounted HUDs, there are also HMDs head-mounted displays. Including Helmet Mounted Displays (both abbreviated HMD), forms of HUD that features a display element that moves with the orientation of the users' heads.Many modern fighters (such as the F/A-18, F-16 and Eurofighter) use both a HUD and HMD concurrently. The F-35 Lightning II was designed without a HUD, relying solely on the HMD, making it the first modern military fighter not to have a fixed HUD

Types

SOLO Head-up Display (HUD(

HUDs are split into four generations reflecting the technology used to generate the images.

• First Generation—Use a CRT to generate an image on a phosphor screen, having the disadvantage of the phosphor screen coating degrading over time. The majority of HUDs in operation today are of this type.• Second Generation—Use a solid state light source, for example LED, which is modulated by an LCD screen to display an image. These systems do not fade or require the high voltages of first generation systems. These systems are on commercial aircraft.• Third Generation—Use optical waveguides to produce images directly in the combiner rather than use a projection system.• Fourth Generation—Use a scanning laser to display images and even video imagery on a clear transparent medium.

Newer micro-display imaging technologies are being introduced, including liquid crystal display (LCD(, liquid crystal on silicon (LCoS(, digital micro-mirrors (DMD(, and organic light-emitting diode (OLED(.

SOLO Airborne Radars

Spick M., “The Great Book of Modern Warplanes”, Salamander, 2003

F/A-18 Head Up Display (HUD(

F-18 HUD Gun Symbology

42



Typical aircraft HUDs display data: Airspeed, Altitude, a Horizon Line, Heading, Turn/Bank and Slip/Skid indicators. These instruments are the minimum required by 14 CFR Part 91.Other symbols and data are also available in some HUDs:• Boresight or Waterline Symbol —is fixed on the display and shows where the nose of the aircraft is actually pointing.• Flight Path Vector (FPV( or Velocity Vector Symbol —shows where the aircraft is actually going, the sum of all forces acting on the aircraft.] For example, if the aircraft is pitched up but is losing energy, then the FPV symbol will be below the horizon even though the boresight symbol is above the horizon. During approach and landing, a pilot can fly the approach by keeping the FPV symbol at the desired descent angle and touchdown point on the runway.• Acceleration Indicator or Energy Cue —typically to the left of the FPV symbol, it is above it if the aircraft is accelerating, and below the FPV symbol if decelerating.• Angle Of Attack indicator —shows the wing's angle relative to the airflow, often displayed as "α".• Navigation Data and Symbols —for approaches and landings, the flight guidance systems can provide visual cues based on navigation aids such as an Instrument Landing System (ILS( or Augmented Global Positioning System such as the Wide Area Augmentation System. Typically this is a circle which fits inside the flight path vector symbol. Pilots can fly along the correct flight path by "flying to" the guidance cue.


1 Available Gs 10 Gun Cross

2 Current Gs 11 Waterline Symbol

3 Mach Ratio 12 Velocity Vector

4 True Airspeed 13 Barometric Altitude

5 Angle of Attack (AOA) 14 Radar Altitude

6 Indicated Airspeed 15 Horizon Line

7 Pitch Ladder 16 Ghost Velocity Vector

8 Command Heading Marker 17 Maximum Projected Area

9 Heading Scale

F-15E - Head-Up Display

F-15C_ M61A1 Vulcan Cannon and AIM-9M Sidewinder


In addition to the generic information described above, military applications include weapons system and sensor data such as:• Target Designation (TD( indicator—places a cue over an air or ground target (which is typically derived from radar or inertial navigation system data(. • Vc—closing velocity with target. • Range—to target, waypoint, etc. • Launch Acceptability Region (LAR(—displays when an air-to-air or air-to-ground weapon can be successfully launched to reach a specified target. • Weapon Seeker or sensor line of sight—shows where a seeker or sensor is pointing. • Weapon status—includes type and number of weapons selected, available, arming, etc.

Military aircraft specific applications

SOLO Airborne Radars

http://www.ausairpower.net/Profile-F-15A-D.html

F-15 Head Up Display (HUD( Data at Different Mission Modes

SOLO

F16

F-16: Enhanced Envelope Gun Sight (EEGS(

SOLO

F16

F-16: Lead Computing Optical Sight (LCOS(

SOLO

F16

F-16: AIM-9 Missile Mode

SOLO

F16

F-16: AIM-120 AMRAAM Missile Mode

SOLO

F16F16 Gunsight

Four different sighting references are available for use:1.Gun Cross2.Lead Computing Optical Sight (LCOS(3.Snap shot Sight (SS(4.Enhanced Envelope Gunsight (EEGS( only for F16C and up.

1. The Gun Cross is always available and easily used. The Pilot can effectively imagine the Gun Cross as being where gun barrels are pointed. Proper Aim is achieved by

positioning the Gun Cross in the Target Plane of Motion (POM( with the proper amount of Lead. The Gun Cross is a very good reference to use to initially establish the Gun in the Target ‘s POM with some amount of lead. As Range decreases the Pilot can refine the Lead Angle by using as reference the LCOS/EEGS Pippers before firing. Without EEGS the Gun Cross is the only usable reference during very high dynamic, high aspect angle shot attempt.

2. The LCOS Pipper represents a Sighting Reference for which the Gun is now properly aimed. With the Pipper. Pipper helps the Pilot to establish th proper Lead Angle to kill the Target. The key LCOS assumption is that the Pilot is tracking the Target with the Pipper. In addition Target acceleration and shooter parameters (Airspeed, Range, G and POM( remain constant during the Time of Flight (TOF(.

SOLO

F16

3. The Snap Shot Display is a historic tracer Gunsight. The principle of the System is to let the Pilot see where the projectiles would be once they have left the Gun. The Snap Shot Algorithm functions completely independent of Target Parameters except range, which is used the Pipper on the Continuously Computed Impact Line (CCIL(. The key is that the System is Historic and not Predictive in nature. It is very hard to use it as an aiming reference and is not recommended because of the TOF lag in the presentation and the difficulty in managing the sight. However, it does provide an excellent shot evaluation capability. The accuracy of the sight is within 4 – 5 mils at 2000’ range as long as the Pilot have not been doing any rapid rolling maneuvers. LCOS and Snap Shot always be called up together when employing the Gun, use LCOS to aim with and Snap Shot to evaluate the shot.

4. The EEGS is a combination LCOS and Director Gunsight available in F16C. It provides the capability to accurately employ the Gun at all aspects, with or without a Radar Lock, against an evasive or predictable Target, and out to maximum Gun Effective Range. The EEGS consists of Five Levels of Displays, each providing an increasing level of capability depending upon Radar knowledge of Target Parameters (Range, Velocity and Acceleration(. As the Radar Locks on to the Target, the Sight Symbology smoothly transitions from Level II to Level V, without any large transient motions typical of LCOS mechanization.

SOLO

F16

F16 HUD, Movie

F-16 Cockpit, avionics and radar, Movie

GR F-16 Vs TURK F-16real video with sound, Movie

EEGS Level 1

The lowest level of symbology, Level I, consists of the Gun Cross and is used in the Event Hud or System Failure. The Symbol is the same as the current LCOSS GunCross.

SOLO

F16

Level II is the basic No-Lock Symbology. It consists of the funnel and the MultipleReference Gunsight (MRGS( lines. In Level II and III, the dynamics of the funnelare based on a traditional LCOS system. Ranging can be obtained from wingspan matching. The funnel is used in low aspect (up to 50 ͦ ( or high aspect (130 ͦ to 180 ͦ( shots to establish the Aircraft in the proper POM and to track the Target. The top of the funnel is 600’ range and the bottom in the between 2500’ and 3000’, depending upon altitude. An accurate aiming solution exists when (1(The Target is being tracked at the point in the funnel where the wingspan is equal to the funnel width (assuming the proper wingspan is set in the DED((2( The shooter rate of turn approaches that of the LOS to the Target.The only assumption here is that the Target is turning into the attack.The Pilot is thereby provided a Sight with a good estimation of proper Lead Angle out to approximately 1500’, where the width and slope of the funnel decreases to the point where wingspan matching is no longer accurate. The MRGS lines are used in high LOS rate attacks (such as Beam Aspect against a High Speed Target(To put the Airc raft in the Target POM with excess Lead. Finally, Level II Symbology includes the Launch Envelopes Display System (LEDS(, simulated rounds which are fired at a rate of five per second while the trigger is depressed and are displayed on the HUD as dot pairs. The dot pairs move downward across the HUD in the same way that tracers would move had they been fired, and their width corresponds to their current range in mils (based on the DED entered wingspan(

EEGS Level II

SOLO

F16

64

References

Anthony L. Leatham, “A Digital Lead Computing Optical Sight Model”, AD-786464, Air Force Academy, 1974

“Multi-Command Handbook 11-F16” Volume 5, Effective Date: 10 May 1996

http://en.wikipedia.org/wiki

AD-A208651, “Evaluation of Head-Up Displays Format for the F/A-18 Hornet”, Leah M. Roust, March 1989 Thesis, Naval Postgraduate School, Montery, CA, USA

65

SOLO

TechnionIsraeli Institute of Technology

1964 – 1968 BSc EE1968 – 1971 MSc EE

Israeli Air Force1970 – 1974

RAFAELIsraeli Armament Development Authority

1974 – 2013

Stanford University1983 – 1986 PhD AA

66

Performance of Aircraft Cannons in terms of their Employment in Air Combat

67


68


69


6 computing gunsight, hud and hms

Science